Asymptotic Behavior of the Kobayashi Metric on Certain Infinite-Type Pseudoconvex Domains in C2 Original Research Article

We study the asymptotic behavior of the Kobayashi metric near boundary points of the exponentially-flat infinite type in bounded domains in C2. These depend upon the tangency of the streams of reference points to the boundary. This is a generalization of Grahamʹs theorem on the asymptotic behavior of the Carathéodory and Kobayashi metrics of bounded strongly pseudoconvex domains in Cn.